Boil the potatoes in salted water until done, about 15-20 minutes. Let them cool down a bit before cutting in half.
Heat a small frying pan over medium high heat and add the half teaspoon olive oil. Add the almonds and roast them, tossing often, until they start to crack and brown a bit. Be careful not to burn then – it happens really quick!. Sprinkle with salt and transfer to a paper towel. Let the almonds cool down before roughly chopping them.
Mix the now lukewarm potatoes with the tomatoes and the almonds in a bowl and season to taste with salt and pepper. Mix the vinegar with the extra virgin olive oil and pour over the potatoes, mix well. Immediately before serving mix in the spinach and toss to mix well.